Abstract
Consider the Deligne-Simpson problem: give necessary and sufficient conditions for the choice of the conjugacy classes C j ∃( n, C) (or C j λ( n, C) so that there exist irreducible (p + 1) -tuples of matrices M j ε C j (or A j ε c j) satisfying the equality m 1 … M p+1 = I (or A 1 + … + A p+1 = 0) . We solve the problem for generic eigenvalues; their set is defined by explicit algebraic inequalities. There exist no reducible ( p + l)-tuples of matrices for generic eigenvalues. The matrices M 1 and A j are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann's sphere.
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